What is the derivative of (2e^x+x^2ln(x)) ?

The derivative of (2e^x+x^2ln(x)) is ln(x)(2e^x+2x)+(2e^x+x^2)/x

What is the first derivative of (2e^x+x^2ln(x)) ?

The first derivative of (2e^x+x^2ln(x)) is ln(x)(2e^x+2x)+(2e^x+x^2)/x

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\frac{d}{d x} ((2 e^{x} + x^{2}) ln (x))

ln (x) (2 e^{x} + 2 x) + \frac{2 e ^{x} + x ^{2}}{x}

Solution steps

\frac{d}{d x} ((2 e^{x} + x^{2}) ln (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 e^{x} + x^{2}, g = ln (x)

= \frac{d}{d x} (2 e^{x} + x^{2}) ln (x) + \frac{d}{d x} (ln (x)) (2 e^{x} + x^{2})

\frac{d}{d x} (2 e^{x} + x^{2}) = 2 e^{x} + 2 x

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= (2 e^{x} + 2 x) ln (x) + \frac{1}{x} (2 e^{x} + x^{2})

\frac{1}{x} (2 e^{x} + x^{2}) = \frac{2 e ^{x} + x ^{2}}{x}

= ln (x) (2 e^{x} + 2 x) + \frac{2 e ^{x} + x ^{2}}{x}

x \to 1 lim (x)

\frac{1}{s ^{2}} - \frac{1}{s} + \frac{1}{( s - 2 )}

\int \frac{x ^{2} + 2 x}{x ^{2} + 2 x + 1} d x

\frac{d}{d x} (x - \frac{3}{x})

\frac{d}{d x} (ln (x + x^{2} - 4))

What is the derivative of (2e^x+x^2ln(x)) ?
The derivative of (2e^x+x^2ln(x)) is ln(x)(2e^x+2x)+(2e^x+x^2)/x
What is the first derivative of (2e^x+x^2ln(x)) ?
The first derivative of (2e^x+x^2ln(x)) is ln(x)(2e^x+2x)+(2e^x+x^2)/x